Streaking Behaviour of Lights - Render but not Viewport
It looks like the render is the physically correct way to render lights over that kind of surface. Looking up reference images of sunsets over an ocean show similar effects. To make the light not travel that far down the surface of your floor, you'll likely need to lower the power of the lights.
I wonder if the floor has a modifier on it that changes it's displacement that would only show up on a real render, and not in your viewport.